Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect. Existence and uniqueness of global-in-time solutions
Słowa kluczowe
Chemotaxis equations, global-in-time existence and uniqueness, quasilinear reaction-diffusion systems, prevention of blow-up, Schauder fixed point theoremAbstrakt
A system of quasilinear non-uniformly parabolic-elliptic equations modelling chemotaxis and taking into account the volume filling effect is studied under no-flux boundary conditions. The proof of existence and uniqueness of a global-in-time weak solution is given. First the local solutions are constructed. This is done by the Schauder fixed point theorem. Uniqueness is proved with the use of the duality method. A priori estimates are stated either in the case when the Lyapunov functional is bounded from below or chemotactic forces are suitably weakened.Pobrania
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2007-06-01
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CIEŚLAK, Tomasz & MORALE-RODRIGO, Cristian. Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect. Existence and uniqueness of global-in-time solutions. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 2007, T. 29, nr 2, s. 361–381. [udostępniono 22.7.2024].
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